Fungrim entry: 90f31e

\operatorname{EssentialSingularities}\!\left(C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \left\{{\tilde \infty}\right\}

Assumptions:

C \in \mathbb{C} \;\mathbin{\operatorname{and}}\; D \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{not} \left(C = 0 \;\mathbin{\operatorname{and}}\; D = 0\right)

TeX:

\operatorname{EssentialSingularities}\!\left(C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \left\{{\tilde \infty}\right\}

C \in \mathbb{C} \;\mathbin{\operatorname{and}}\; D \in \mathbb{C} \;\mathbin{\operatorname{and}}\;  \operatorname{not} \left(C = 0 \;\mathbin{\operatorname{and}}\; D = 0\right)

Definitions:

Fungrim symbol	Notation	Short description
`AiryAi`	$\operatorname{Ai}\!\left(z\right)$	Airy function of the first kind
`AiryBi`	$\operatorname{Bi}\!\left(z\right)$	Airy function of the second kind
`CC`	$\mathbb{C}$	Complex numbers
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity

Source code for this entry:

Entry(ID("90f31e"),
    Formula(Equal(EssentialSingularities(Add(Mul(C, AiryAi(z)), Mul(D, AiryBi(z))), z, Union(CC, Set(UnsignedInfinity))), Set(UnsignedInfinity))),
    Variables(C, D),
    Assumptions(And(Element(C, CC), Element(D, CC), Not(And(Equal(C, 0), Equal(D, 0))))))

Topics using this entry

Airy functions